Finding Node Voltages Using the Node Method

erok81

1. The problem statement, all variables and given/known data

Find the node voltages for the circuit shown.

2. Relevant equations

See attachment.

3. The attempt at a solution

I have chosen my ground node as the set of nodes in the bottom of the image and labeled all of my unknown voltages as e_n.

Here is what I have so far. Where G = 1/R

For the node labeled e₁:

(e₁-v₀)G₁ + e₁(G₃) + (e₁-e₂)I₁ + (e₁-e₂)G₂=0

For the node labeled e₂:

(e₂-e₁)(-I₂) + e₂(G₄) + (e₂-e₁)G₂=0

I am pretty sure my problem lies in the way I am handling the currents in the node. I started plugging in numbers after I simplified it all and one of my unknown voltages went away. After that I looked at it again and knew I was doing it wrong. Most of the examples in the book don't deal with a current parallel to a resistor.

I think the way I should have done it is rather than subtracting voltages and multiplying like I am doing with the resistor nodes, is just take the current by itself.

So in my above equation e₁)(-I₁) would just become -I₁ since I am not using ohms law for current. I think I only need current? Does that sound better?

Attached Thumbnails

 

gneill

Yup. Much better. Voltage x current yields power, not a current, so is quite unsuitable for a KCL expression!

erok81

Perfect! Thanks for the help.

It seems half the time I post problems, I get them mostly figured out just typing the post up. :)

gneill

Yup. Typing it out so that it make sense to someone else can often help one re-evaluate one's logic and assumptions.